How do you factor #x^ { 3} - 6x ^ { 2} + 5x#?

2 Answers
Jim G.
Mar 27, 2018

#x(x-5)(x-1)#

Explanation:

#"take out a "color(blue)"common factor "x#

#rArrx(x^2-6x+5)larrcolor(blue)"factor the quadratic"#

#"the factors of + 5 which sum to - 6 are - 5 and - 1"#

#rArrx^2-6x+5=(x-5)(x-1)#

#rArrx^3-6x^2+5x=x(x-5)(x-1)#

Somebody N.
Mar 27, 2018

#color(blue)(x(x-5)(x-1)#

Explanation:

First factor out #x#. This will then leave you with a quadratic, which is easier to factor:

#x^3-6x^2+5x#

#x(x^2-6x+5)#

Factor #x^2-6x+5#:

#x^2-5x-x+5#

#x(x-5)-(x-5)#

#(x-5)[x-1]#

#(x-5)(x-1)#

#:.#

#color(blue)(x(x-5)(x-1)#

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